The Green’s function codes (lmgf, the GW and DMFT codes) are somewhat more complicated, as the bands are broadened, either through alloy scattering (CPA) or through many-body electron-electron interactions. Interacting energy bands for Fe generated by the fully dynamical self-energy are generated in this tutorial, and those for La2CuO4 generated by DMFT are explained in this tutorial.

The plbnds utility is a very useful tool to render the bands generated by band codes in an easy-to read format for graphics packages to make figures with. It automatically makes a script for Questaal’s fplot (graphics utility). The plbnds documentation offers several examples.

Drawing Fermi Surfaces

Fermi surfaces can be drawn with the lmf and lm codes. See this tutorial.

All of the band codes (lmf, lm, and tbe) have the ability to generate the total Density of States (DOS). Total DOS are automatically generated when you set BZ_SAVDOS. DOS are written to file dos.ext (one DOS in the nonmagnetic case and two in the spin-polarized case). Note: this switch will not be active if BZ_METAL is zero. You can also make the DOS using the command-line switch --dos as described in this tutorial.

The pldos utility will render dos.ext into more user friendly formats, and perform other functions.

Questaal codes lmf and lm can resolve densities-of-states into partial contributions, either by projecting onto partial waves in augmentation spheres, or by Mulliken analysis. Questaal can also perform Core-Level Spectroscopy (CLS), also known as EELS, which is closely related to the DOS.

Accomplish these by adding one of following switches to the commmand-line:

All the switches have several options; for --pdos and --mull see here; for --cls see here.

Tutorials for partial DOS, Mulliken analysis, and core-level spectroscopy, can be found on this page.

For k-resolved DOS, and as well as joint projection of k resolved and Mulliken resolved DOS onto orbitals, see this tutorial.

lmgf and lmpg can make partial DOS. They can either do it by Pade extrapolation to the real axis of the imaginary part of the Green’s function calculated on the contour in the complex plane, or you can choose a contour close to the real axis and generate DOS directly. The latter is more accurate, but more time consuming. For a demonstration, try

$ ~/lm/gf/test/test.gf nife

Spectral Functions

DOS are equivalent to spectral functions, though generally spectral functions refer to DOS when there is some scattering to spread out the pole δ(E−E0)\delta(E - E_0)δ(E−E​0​​) in Im(G)Im(G)Im(G) from a noninteracting eigenstate at energy E0E_0E​0​​.

Codes calculate spectral functions for interacting electrons in several contexts:

The ASA Green’s function code lmgf will calculate spectral functions in the context of the Coherent Potential Approximation, see this document. Electrons aren’t interacting in the many-body sense here; disorder causes scattering which has the same effect.

The following provides an extensive test of SO coupling, resolving contribution by site, and scaling λL⋅S⟩\lambda L \cdot S\rangleλL⋅S⟩ to extract the dependence on λ\lambdaλ

$ ~/lm/fp/test/test.fp coptso

Fully Relativistic Dirac Equation

The Dirac equation is implemented in the ASA, in codes lm and lmgf.

There is no tutorial as yet. See this demonstration:

$ ~/lm/gf/test/test.frgf ni

lmfa will generate core levels from the Dirac equation. See this tutorial.

Application of External Scalar Potential

For the lmf code, try the following demonstration:

$ ~/lm/fp/test/test.fp mgo

Fixed spin-moment

One technique stabilize self-consistency in difficut magnetic calculations, or to extract quantities such as the magnetic susceptibility, you can imposed a fixed magnetic moment by imposing distinct Fermi levels for each spin. This is equivalent to imposing a static, q>=0q >= 0q>=0 Zeeman field.

Adding a Homogenous Background Density

Try the following demonstration:

$ ~/lm/fp/test/test.fp c

Band Edge and Effective Mass Finder

Finding band edges in complex semiconductors and insulators can be a tedious exercise. This tutorial explains a tool that automates the process and also gives effective mass tensors around band extrema.

Spin Dynamics

Phonons

Other Notes

Techniques for Brillouin Zone Integration

Techniques for Brillouin zone integration are described some detail here.

How to Make Integer Lists in Various Contexts

The syntax for integer lists is described here. In some contexts lists can consist of real numbers. The same rules apply.

How to Define Rotations in Various Contexts

Rotations are used for crystal axes, spin quantization axes, and in a few other contexts. They are constructed by a succession of angles around specified axes. This page explains how to specify rotations.

How Site Positions are Read by the Input File

Lattice data (lattice vectors and site positions) can be read in different ways. See this page.

Angular Momentum in the Questaal suite

Questaal codes use real harmonics YlmY_{lm}Y​lm​​ by default, which are real linear combination of spherical harmonics YlmY_{lm}Y​lm​​. The ASA codes will, however, use true spherical harmonics if you set OPTIONS_SHARM to true.

The YlmY_{lm}Y​lm​​ are functions of solid angle, while YlmrlY_{lm}r^lY​lm​​r​l​​ are polynomials in xxx, yyy, and zzz. This page documents Questaal’s conventions for real and spherical harmonics and shows the polynomial forms of hte YlmY_{lm}Y​lm​​ for l=0...3l = 0...3l=0...3.